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Chaotic transport and trapping close to regular structures in 4D symplectic maps

Higher-dimensional Hamiltonian systems usually exhibit a mixed phase space in which regular and chaotic motion coexist. While regular trajectories are confined to regular tori, chaotic trajectories can be transported through a web of so called resonance channels which disrupt the regular structures. The focus of this thesis are time-discrete 4D symplectic maps which represent the lowest dimensional system for which the chaotic transport can circumvent regular tori. While the dynamics of 2D maps are well established, many fundamental questions are open for maps of dimension four and higher due to this property. In particular, the mechanism of the power-law trapping is unknown for these maps. In this thesis, the organization and hierarchy of the regular structures of 4D maps is uncovered and the slow chaotic transport close to these structures is examined. Specifically, this transport is shown to be organized by a set of overlapping resonance channels. The transport across these channels is found to be governed by partial transport barriers. For the transport along a channel a stochastic process including a drift is conjectured. Based on each of these two types of chaotic transport a possible mechanism for the power-law trapping in higher-dimensional systems is proposed.

Identiferoai:union.ndltd.org:DRESDEN/oai:qucosa:de:qucosa:29708
Date08 August 2016
CreatorsLange, Steffen
ContributorsKetzmerick, Roland, Meiss, James, Technische Universität Dresden
Source SetsHochschulschriftenserver (HSSS) der SLUB Dresden
LanguageEnglish
Detected LanguageEnglish
Typedoc-type:doctoralThesis, info:eu-repo/semantics/doctoralThesis, doc-type:Text
Rightsinfo:eu-repo/semantics/openAccess

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